Intermediate-grades teachers can use these problem sets for assessment, instruction, or additional practice for students. While the problems were originally created for third-grade students, they can also be used in other grades to increase students ‘experience with problems involving groups of items.

There are multiple problems in each file and multiple problems per page. There is space on each page for students to write.

These problem sets include a variety of problems related to multiplicative concepts including whole numbers and fractions. Collectively, these word problems address standards and benchmarks related to the strands of Number Sense and Operations, Fractions, and Algebraic Reasoning. Multiplication problems and measurement-division types of problem—those in which we know the quantity of each group but not how many groups there are—assist with assessment and development of children’s understanding of multidigit numbers and base-ten concepts (especially when they involve groups of ten). Partitive division or equal-sharing problems, on the other hand, can support assessment and development of children’s understanding of fractions (and rational numbers in general). For more information about these types of problems, Children’s Mathematics: Cognitively Guided Instruction by Thomas P. Carpenter et al. and Extending Children’s Mathematics: Fractions and Decimals by Susan B. Empson and Linda Levi provide more information about the types of problems and how children’s solution strategies can yield insight into their mathematical understanding.

Many thanks to Lorey Pipkorn, a third-grade teacher in Bay District Schools. Lorey wrote the original versions of these problems and offered to share them with the TiPS community!

These sets of problems have a Creative Commons License. That means that you may use these and adapt the problems and/or the layout to meet your own purposes or the needs of your classroom. It also means that you may not sell them or claim the intellectual property therein for you own.

Future versions may be provided with blank spaces in the text of the problems and several combinations of numbers that students may choose to use in order to adjust the level of difficulty to an optimal level of challenge.

We are providing them in pdf format or in Word format in case you want to adapt them. For suggestions or additional requests, please contact Naomi Iuhasz at Velezniuhaszvelez@fsu.edu.

 Multiplicative Concepts Problem Set 1 Multiplicative Concepts Problem Set 2 Multiplicative Concepts Problem Set 3 Multiplicative Concepts Problem Set 4